Polymers mixing entropy

Due to the smallness of the entropy of mixing, most polymer mixtures are at least partially incompatible, and blends contain A-rich and B-rich domains, separated by interfaces. The intrinsic width of these interfaces is rather broad (it varies from w = aJin... 

The entropy of mixing disoriented polymer and solvent may be obtained, according to the original assumptions pertaining to the lattice model, by subtracting Eq. (9) from (8). The result reduces to ... 

One practical example of demixing that might be attributed to a difference in crystallizability is the incompatibility in blends of polymers with different stereochemical compositions. The stereochemical isomers contain both chemical and geometrical similarities, but differ in the tendency of close packing. In this case, both the mixing energy B and the additional mixing entropy due to structural asymmetry between two kinds of monomers are small. However, the stereochemical differences between two polymers will result in a difference in the value of Ep. Under this consideration, most experimental observations on the compatibility of polymer blends with different stereochemical compositions [89-99] are tractable. For more details, we refer the reader to Ref. [86]. 

Equation (9.55) is the expression for the entropy of mixing of polymer solutions introduced first by Flory [7], Nm and iVp can be related through x m + Xp = 1, which for one mole of molecules (polymers + monomers) gives... 

Wang, W., Manas-Zloczower, I., and Kaufman, M., Characterization of Distributive Mixing in Polymer Processing Equipment using Renyi Entropies, Int. Polym. Process., 16, 315 (2001)... 

Miscible blends are not as easy to achieve as immiscible blends. As noted above, entropy is the major driving force in causing materials to mix. Because polymer chains are already in a state of relatively high order, increases in randomness are not easily achieved so that immiscible blends are often more easily formed. To make matters worse, for amorphous polymers the amount of disorder in the unmixed polymer is often higher than for blends that tend to arrange the polymer chains in a more ordered fashion. 

Flory [3] formalized the equation of state for equilibrium swelling of gels. It consists of four terms the term of rubber-like elasticity, the term of mixing entropy, the term of polymer solvent interaction and the term of osmotic pressure due to free counter ions. Therefore, the gel volume is strongly influenced by temperature, the kind of solvent, free ion concentrations and the degree of dissociation of groups on polymer chains. 

The entropy of mixing disoriented polymer and solvent may be obtained ... 

Equation (12-16) is similar to Eq. (12-1), except that volume fractions have replaced mole fractions. This difference reflects the fact that the entropy of mixing of polymers is small compared to that of micromolecules because there are fewer possible arrangements of solvent molecules and polymer segments than there would be if the segments were not connected to each other. 

Only a limited number of solvents can be used for rigid-chain polymers because of small changes in the entropy term of the free energy of mixing a polymer with a solvent. For this reason, the solvents used predominantly are those which interact with active groups in the polymer chains very intensively. 

Despite the fact that the mixing entropy is small for polymer blends, it is always positive and hence promotes mixing. Mixtures with no difference in interaction energy between components are called ideal mixtures. Let us denote the volume fraction of component A by — and the corresponding volume fraction of component B becomes = 1 — The free energy of mixing per site for ideal mixtures is purely entropic ... 

The mixing entropy calculated above includes only the translational entropy that results from the many possible locations for the centre of mass of each component. The calculation assumes that the conformational entropy of a polymer is identical in the mixed and pure states. This assumption is very good for polymer blends, where each chain is nearly... 

Polymer blends have received considerable industrial and academic attention in recent years. Ideally, two or more polymers may be blended to form a wide variety of morphologies that offer potentially desirable combinations of properties. However, it is often not possible to achieve useful compositions because of the unfavorable thermodynamics of mixing of polymers. The entropy of... 

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